1. Surface Area & Volume
Prism & Cylinders

2. A polyhedron (3D shape) has faces that are polygons (2D shape)
- Poly means many; hedron means faces
Two faces meet at an edge
Three or more edges meet at a vertex
Vertex
Edge

3. A net is a two-dimensional figure that, when folded, forms a three-dimensional figure
This is an animation showing the net on the last page to assist with the idea that it forms a cube

4. Nets of a Cube
This is the answer.

5. Prism: A solid object that has two identical ends (bases) and all flat sides
Discuss the idea of bases also refer to the previous slide and discuss how in a rectangular prism you can technically use any pare of parallel sides as the bases. Typically people view the base as the pair that can be considered the top and the bottom of the rectangular prism.
Triangular Prism

6. Prism Names
Rectangular prism
Triangular prism
Height
Height
Base
Base

7. Name the prism

8. Rectangular Prism Base 2 Bottom Back Top Base 1 Front Top Back Side 2
Height (H)
Bottom
In this slide you begin the development of what is surface area. The shape will be broken up identify what shapes make up the outer surface of this shape. Also discuss what the shape is. It will break up into its rectangular parts as it does discuss the opposite sides and their relationship.
Base (B)
Length (L)

9. Example: Rectangular Prism Net

10. Surface Area - the total area of all the faces (surfaces) of an object.
To find the surface area of an object we can add up the areas of the separate faces. Note: some faces have the same size and shape
Surface Area of this prism:
Add the areas of the two brown sides (A) to the two green sides (D) and to the two red sides (C). C D A w h l
This is a rectangular prism. The l, w and h have different values.

11. Surface Area
Find the surface area of the rectangular prism
We should use a table to tabulate the various areas.
Face
Area
Number of Sides
Total Area A
12cm2 2
24cm2 D
15cm2
30cm2 C
20cm2
40cm2
TOTAL 6
94cm2 C D A
3 cm
5 cm
4 cm
Area of rectangle = l x w

12. Volume
5 cm B B
2 cm B h h h
The number of cubic units needed to fill the space occupied by a solid.
3 cm
VOLUME OF A PRISM
The volume V of a prism is the area of its base B times its height h.
V = Bh
Note – the capital letter stands for the AREA of the BASE not the linear measurement.
Volume = Base area x height
= (l x w) x height
= (3 cm x 2 cm) x height
= 6 cm2 x 5 cm
= 30 cm3
Discuss why this is a unit cube and the volume vormula
Area of rectangle = l x w

13. Prism Volume Example V = Bh = (4ft x 3ft)h = (12 ft2)h
Find area of the base 1st
= (4ft x 3ft)h
= (12 ft2)h
Multiply it by the height
= (12 ft2) x 8 ft
= 96 ft3
3 ft B
4 ft
8 ft
Area of rectangle = l x w

14. What is the surface area and volume of the prism?
SA rectangle = l x w
SA (rect1) = 12 cm x 10 cm
= 120 cm2 x 2 = 240 cm2
SA (rect2) = 12 cm2 x 22 cm
= 264 cm2 x 2 = 528 cm2
SA (rect3) = 10 cm x 22 cm2
= 220 cm2 x 2 = 440 cm2
Total SA = SA (rect1) + SA (rect2) + SA(rect3)
= 240 cm cm cm2
= cm2
10 cm B
12 cm
22 cm
V = Bh
= (12 cm x 10 cm) x h
= (120 cm2) x 22 cm
= 2640 cm3
Note Units

15. Example Nets For Triangular Prisms

16. Surface Area of a triangular prism
2 area of same triangle + 2 areas of 3 rectangles, which 2 are the same
15ft
Area Triangle 1 & 2 = 𝑏ℎ 2
= 12 𝑓𝑡 𝑥 15 𝑓𝑡 2
= 180 ft2 2
= 90 ft2
Area Rect. 1 = l x w
= 12 ft x 25 ft
= 300 ft2
Area Rect. 2 & 3 = 25 ft x 20 ft
= 500 ft2
SA=triangle1 + triangle2 + rectangle1 + rectangle2 + rectangle3
SA=
+ 300
+ 500
+ 500
SA = 1480 ft2

17. Volume of a triangular prism
Area Triangles = 𝒃𝒉 𝟐
= 𝟏𝟐 𝒙 𝟏𝟓 𝟐
= 𝟏𝟖𝟎 𝟐
= 90 ft2
V= Bh
Find area of the base
= (90 ft2)h
Multiply it by the height
= (90 ft2) x 25 ft
= 2250 ft3
15ft

18. Classwork Page 186-188 #4, 5, 6a, 7a Page 192-193 #4,6,8

19. Cylinder Bases Cylinder
Discuss how prisms and cylinders have similar ways of looking at the base they are congruent parrallel and there are 2.
Cylinder

20. SA of a Cylinder
Formula for Area of Circle
A=  r2
= 3.14 x 32
= 3.14 x 9
= 28.26
But there are 2 of them so
28.26 x 2 = units squared
Find the circumference to determine the length of the rectangle
C =  x d
= 3.14 x 6 (radius doubled)
= 18.84
Now use that as your base.
A = b x h
= x 6 (the height given)
= units squared
Now add the area of the circles and the area of the rectangle together.
= units squared
The total Surface Area!

21. Volume of a Cylinder = (28.26)h = 169.56 unit3 V= Bh
Formula for Area of Circle
A=  r2
= 3.14 x 32
= 3.14 x 9
= unit2
V= Bh
Find area of the base
= (28.26)h
Multiply it by the height
= (28.26) x 6
= unit3

22. Calculate the SA and Volume of the cylinder Be sure you know the difference between a radius and a diameter!
Formula for Area of Circle
A=  r2
= 3.14 x 52
= 3.14 x 25
= 78.54
But there are 2 of them so
78.54 x 2 = units squared
V = Bh
C =  x d
= x 10 (radius doubled)
= 31.15
Now use that as your base.
A = b x h
= x 4.2 (the height given)
= units squared
The radius of the cylinder is 5 m, and the height is 4.2 m; therefore B = A =  r = 3.14 · 52 = m2
V = Bh
V = · 4.2
V = m3
SA = = m2

23. Classwork
Page #4,8,9